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Carrier capture times in 1.5 pm -multiple quantum well optical amplifiers S. Weisqa) J. M. Wiesenfeld, D. S. Chemla,a) G. Raybon, G. Sucha,a) M. We ener,b) G. Eisenstein ‘) C. A. Burrus, A. G. Dentai, U. Koren, B. I. Miller, H. Temkin, # R. A. Logan,dj and T. Tanbun-Ekd) AT&T Bell Laboratories, Holmdel, New Jersey 07733 (Received 19 August 1991; accepted for publication 21 October 1991) The carrier capture times in multiple quantum well semiconductor amplifiers of different structures are studied under high plasma density conditions. Fast ( < 1 ps), slow ( > 150 ps), and intermediate time constants (2-7 ps) are identified in InGaAs qtiantum well structures. The intermediate time constant is attributed to carrier diffusion in the cladding layers and identified as the carrier capture time. Short capture times can be achieved by proper design of the device structire. The capture times of carriers into quantum wells (QW) have been the subject of several studies in the last few years. These studies are motivated by both practical and fundamental reasons. It was suggested, only recently, that the capture time into the QWs is directly related to the nonlinear gain compression observed in these lasers.’ The nonlinear gain compression factor E is a phenomenological parameter that is inserted in the rate equations model of the laser to explain the nonlinearity of its gain. While the physics behind E is far from understood, it has been found that by introducing this parameter one can model quite well the damping behavior of lasers at high frequencies.” For bulk lasers, it was suggested that spectral hole burning3 and/or carrier heating’ are the mechanisms underlying nonlinear gain compression. For QW lasers, however, the magnitude of E is often larger than for bulk lasers and therefore cannot be explained solely by the above mechanisms.’ An additional mechanism, related to the carrier capture time in the QW, may explain the observed increase in E for QW lasers. The capture process has been studied experimentally by photoluminescence, photoluminescence excitation,5 and time-resolved luminescence6 spectroscopies on specially designed QW structures, where the carriers were introduced into the sample by optical excitation. The theoretical efforts that followed these experiments took two different approaches. The semiclassical approach’ shows that the capture efficiency decreases when the QW width becomes smaller than the optical phonon limited mean-free path. More elaborate quantum mechanical approaches,8 which calculate the scattering rates into the QWs by taking into account the longitudinal optical (LO) phonon coupling into the final QW states, predict strong oscillations in the capture time as a function of the well width. The singleparticle picture, however, cannot account for the manybody effects in a real, active laser structure and, in particular, does not consider the effects of carrier-carrier scattering. Our experiments are designed to study carrier capture in active laser devices in exactly that regime, by @Present address: Lawrence Berkeley Laboratory, Berkeley, CA 94720. b)Present address: Fachbereich Physik, Universitat Dortmund, Dortmud, Germany. ‘)Present address: Dept. of Elect. Eng., Trchnion, Haifa 32000, Israel. d)Presentaddress:AT&T Bell Laboratories,Murray Hill, NJ 07974. 9 measuring gain recovery dynamics subsequent to gain compression caused by an intense, ultrashort optical pulse. We investigated six samples with different geometries. In Fig. 1 we show the band gap structures of the samples. The first four MOCVD-grown samples (samples 1 to 4), Fig. 1 (a), are separate confinement heterostructures, consisting of a few (four for samples 1, 3, and 4, three for sample 2) In,Ga, _ ,& QVys, separated by InGaAsP barrier layers with a 0.95 eV band gap (il,, = 1.3 pm). On both sides of the multiple QW structure are InGaAsP cladding layers with the same composition as the barriers. These cladding layers define the optical waveguide and store the carriers. For the latter reason, we henceforth call them the “reservoir” (RES) . The contact layers consist of InP. The QWs of samples 2 and 3 are compressively strained (X = 0.77), whereas those of samples 1 and 4 are unstrained (x = 0.53). The widths of the QW, the barriers and the RES are listed in Table I. The transition from the /I RI%= 1.3 pm layers to the InP layers was either with a single step, Fig. 1 (a), or a few discrete steps [not shown in Fig. 1 (a)]. We also had one graded gap (and index) sample which was compressively strained (x=0.66), 5 and Fig. 1 (b), and a control sample, with no QWs (conv&ntional LPE-grown V-groove laser’), 6 and Fig. 1 (c) . Highquality antireflection SiO, coatings (reflectivity < 10 - 3, were deposited on both facets of the samples to make optical amplifiers. With these coatings it is possible to inject a very high current density with no clamping of the population inversion. This was experimentally verified by measuring the spectrum of the amplified spontaneous emission of the processed samples.” From these measurements we estimate a carrier density in the QWs close to or in excess of 1019 cm ~ 3 under high current injection ( -200-300 mA for .- 500 pm-long devices). That high density implies that the average distance between carriers is -50 A, i.e., ( the Bohr radius of the excitons in the QWs. The gain recovery dynamics were measured by a pump-probe technique, using 0.4 ps duration pulses from an additive pulse modelocked (APM) color center laser,” operating at 76 MHz repetition rate. The pump pulse was polarized perpendicular to the junction plane of the amplifier (TM polarization) and orthogonal to the probe pulse (TE polarization). With this arrangement of beam polarizations, the test beam probes the TE gain dynamics.” Appl. Phys. Lett. 60 (I), 6 January 1992 0003-6951/92/010009-03$03.00 @ 1992 American Institute of Physics 9 Downloaded 27 Jan 2004 to 132.68.1.29. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp sample #6 I time (ps) FIG. 2. Typical time resolved gain recovery spectra for the control sample 6, for sample 1, and for sample 3. InGaAsP (1.55 pm) FIG. 1. The band gap structure of the semiconductor amplifiers used in the experiment. The QW samples l-4 (a), the graded index sample 5(b) and the control sample 6(c), which has no QWs but an InGaAsP active layer. Pump and probe beams were combined in a fiber directional coupler and coupled into the amplifier using a fiber with a microlens. The pump pulse energy at the amplifier input was 4 pJ or less, producing up to 8 dB of gain compression, and was at least 100 times more intense than the probe. The pump pulse removes carriers form the bottom of the QWs, primarily by stimulated emission, but also by free carrier absorption. The recovery of the gain is then monitored by the probe pulse. In principle, one should distinguish the following sequence in the carrier dynamics: Immediately after the removal of the carriers,” the remaining population of carriers in the QWs is nonthermal. Those carriers first thermalize among themselves (hole burning .- 10-100 fs). Then, they thermalize with the lattice (carps). Recently, an intermediate time rier cooling -0.7-l constant ( - 250 fs) was measured and attributed to carrier heating and/or hole burning.” Next, as has been shown in previous work,” the carriers from the RES replenish those that were removed from the QW by the pump on a 2-10 ps time scale. Finally, carriers from the contacts reestablish the steady-state population, on a time scale of few hunTABLE I. Summary of the samples’ parameters and dimensions. Total I 1 2 3 4 5 6 2620 2655 1570 1535 800a 2400b 2000 2400 1200 500 2200 2400b I yrj” yr; 80(x4) 25(x3) 25(X4) 90(X4) 30(X4) 2400b 100(X3) 90(X2) 90(X3) 225(X3) 225(x3) ... Strain (46) Carrier capture time (PS) no yes(1.53%) yes(1.53%) ye$:3%) IlO ‘At the bottom of the RES. ‘For this sample, the active layer thickness = total clad = la,. 10 Appl. Phys. Lett.. Vol. 60, No. 1, 6 January 1992 7 4.5 2 4 14 0 dreds of picoseconds, limited by Auger recombination.” Typical time-resolved gain measurements, taken on three different devices, are shown in Fig. 2. We plot gain compression, in dB, as a function of the time delay between the pump and the probe. Both the strained and the nonstrained samples were showing the same qualitative dynamics. The three traces are arbitrarily displaced on the vertical axis, for clarity. The upper trace (device 6), taken on the bulk amplifier, shows only a fast recovery (attributed to carrier cooling1”‘3), on the order of 1 ps, and a very slow recovery ( 170 ps), hardly resolved in Fig. 2, which is Auger recombination limited. The center and the lower traces, taken on devices 1 and 3, respectively, show, in addition to fast ( < 1 ps) and slow ( > 150 ps) time constants, an intermediate time constant, which we attribute to carrier diffusion in the reservoir. This intermediate time constant, which we identify as the carrier capture time, has values of 7 and 2 ps for the curves shown for devices 1 and 3, respectively. Values of the intermediate time constant for all the devices are plotted in Fig. 3 as a function of the square of the reservoir width lREs based on 20 .,.,.I.I.I.I.I.I.I. 18 16 14 -2 ; x F p cc 12 10 6 4 2 0 0 2 4 6 8 10 (l~27T)2(a"gstrom5 12 14 16 18 20 x 10' FIG. 3. Capture time, for all six devices under study, as function of the square of the reservoir width &s. The horizontal error bars for samples S and 6 represent the uncertainty in these values. Weiss et al. Downloaded 27 Jan 2004 to 132.68.1.29. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp 10 the predictions of our model.14 The data points shown are the averages of many independent measurements of the time constants for different values of amplifier bias, pump intensity, and pump wavelength. As long as the bias of the amplifier is sufficiently high to place the Fermi level in the RES, the measured time constants are independent of the above parameters. The carrier capture process includes carrier transport in the RES and inelastic scattering from the RES to the QW. The latter process is referred to as a “local capture time,” while the sum of all processes is the “overall capture time.” The theory used to calculate the quantum mechanical capture time assumes that electrons and holes are in coherent states in the QW and the RES, and it uses the Fermi golden rule to calculate the transition rate between the RES and QW states caused by various coupling mechanisms, such as the emission of LO-phonons. The predicted oscillations in the capture times originate essentially from corresponding oscillations in the wave function overlap. This procedure may be legitimate at vanishingly small densities, i.e., when the photocarriers have the possibility of establishing coherent wave functions. We argue that, at the very large densities encountered in laser amplifiers, carrier-carrier scattering induces such a lifetime broadening of the quantum states that, for RES large enough, the carriers, and especially those at the bottom of the RES, can be treated as a classical fluid.14 Thus, their dynamics is better described in terms of diffusion. The reservoir states are rapidly depopulated locally above the QWs by the emission of LO phonons, but are repopulated almost instantly due to elastic and inelastic scattering processes. Therefore, the overall capture time will be limited by the macroscopic transport properties of the carriers in the RES, namely, diffusion. I5 We modeled the gain recovery dynamics, assuming that the rate limiting step is diffusion. Thus, the relevant time constant is the time required to till in a “hole” created at time zero at the center of a distribution of classical carriers, which occupies a region of width IRES.This time constant was calculated applying standard diffusion theory.14V16The model predicts that the capture time depends on the reservoir width, as 71) = (&/27r) 2/D, where D is the ambipolar diffusion constant. The fit to this model is shown in Fig. 3, where the first four samples ( 1 to 4) fall on the same line, whose slope gives D=2.9 cm2/s; this value is in good agreement with the ambipolar diffusion constant for 1nGaAsP.t’ The bulk sample (6)) of course, does not show up on the line, since there is no vertical transport or diffusion involved in this sample. A surprising result, however, is the measured capture time for the graded index sample (5). The common belief is that carrier capture in this structure is faster than in nongraded struo tures and, indeed, there are some experimental data that support this belief.6 The reason for the slower capture time for our graded index sample is not clear, and more systematic study needs to be done. We propose, nonetheless, a possible explanation. The local (quantum mechanical) capture time will show up as the dominant capture time only when the carriers can establish a coherent quantum 11 state in the RES. Such will be the case when either collisions are rare (low density) or the width of the RES is small (the reservoir dimensions are comparable to those of the QW>.14 The latter case occurs for the graded index sample, because ZREsat the bottom of the reservoir is only 800 A. It is possible that the slow time constant measured for this sample is related to the quantum mechanical oscillations in the capture time.’ In summary, we have shown that the capture time into the QWs is, under normal operating conditions, diffusion limited. To obtain the shortest possible capture time (and the smallest nonlinear gain compression factor) in high speed lasers, the design of the structure must take into account both diffusion and quantum mechanical considerations. The experimental results demonstrate, however, that rapid gain recovery can be engineered into the device structure. We would like to acknowledge D. W. Taylor for his technical help with the data acquisition software. During this work S. Weiss was partially supported by the Rothschild fellowship. ’W. Sharfin, J. Schlafer, W. Rideout, B. Elman, E. Koteles, R. B. Lauer, J. LaCourse, and F. D. Crawford, presented at Conference on Lasers and Electra-Optics, CLEO 91, May 12-17, Baltimore, Maryland. ‘R. S. 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Brum and G. Bastard, Phys. Rev. B 33, 1420 ( 1986); 34, 238 1 (1986); M. Babiker and B. K. Ridley, Superlattices and Microstructures 2, 287 (1986); Semicond. Sci. Technol. 2, 582 (1987); Y. Murayama, Phys. Rev. B 34, 2500 (1986). ‘N. K. Dutta, D. P. Wilt, P. Besomi, W. C. Dautremont-Smith, P. D. Wright, and R. J. Nelson, Appl. Phys. Lett. 44, 483 (1984). ‘OG. Eisenstein, J. M. Wiesenfeld, M. Wegener, G. Sucha, D. S. Chemla, S. Weiss, G. Raybon, and U. Koren, Appl. Phys. Lett. 58, 158 (1991). “J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, and E. P. Ippen, Opt. Lett. 14, 48 (1989). “K. L. Hall, J. Mark, E. P. Ippen, and G. Eisenstein, Appl. Phys. Lett. 56, 1740 (1990); 57, 129, 2888 (1990). ‘“M S Stix, M. P. Kesler, and E. P. Ippen, Appl. Phys. Lett. 48, 1722 (1986). “J. M. Wiesenfeld, S. Weiss, and D. S. Chemla (unpublished). “A. Weller, P. Thomas, J. Feldmann, G. Peter, and E. 0. Gobel, Appl. Phys. A 48, 509 (1989). 16J. Crank, The Mathematics of DIffision, 2nd ed. (Oxford Unviversity Press, New York, 1975). Appl. Phys. Lett., Vol. 60, No. 1, 6 January 1992 Weiss et al. il Downloaded 27 Jan 2004 to 132.68.1.29. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp